List questions from totient-function

Published on 11 Jun 2018 - 23:07

251

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On the equation $\varphi(n)=\left(\frac{1+\sqrt{1+8n}}{8}\right)\cdot\left(\operatorname{rad}(n)-\frac{1+\sqrt{1+8n}}{2}\right)$

Published on 25 Mar 2026 - 15:42

46

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Prove or refute that $\sum_{n=1}^\infty\frac{1}{n^2+A\varphi(n)+B}$ will be irrational for some choice of integers $A,B\geq 1$

Published on 25 Mar 2026 - 12:21

255

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RSA decryption coefficient

Published on 25 Mar 2026 - 12:45

62

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An asymptotic about the recurrence $a_{n+1}=n\varphi(a_n)+a_{\varphi(n)}$, with $a_1=1$ and being $\varphi(m)$ the Euler's totient function

Published on 17 Jun 2018 - 18:39

73

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Euler Totient Integer Remainder Sum Lemma

Published on 18 Jun 2018 - 22:08

65

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Totient values of consecutive positive integers forming a pythagorean triple

Published on 21 Jun 2018 - 11:09

54

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A conjecture about Euler's function

Published on 22 Jun 2018 - 8:30

60

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Around the equation $4\,\varphi \left(2^{n-1} \sigma(n)\right) ^2=2^{\sigma(n)}\cdot\varphi(n)^2$

Published on 25 Mar 2026 - 6:05

87

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Calculate modulo solution of a number with a high exponent

Published on 26 Jun 2018 - 18:49

141

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Does a number have a primitive root if and only if φ(n)=λ(n)?

Published on 25 Mar 2026 - 5:41

64

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Do $4$ consecutive positive integers with square totient-value exist?

Published on 09 Jul 2018 - 8:18

102

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Conditions for computing $n$ given $\varphi\left(n\right)$

Published on 12 Jul 2018 - 18:49

279

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Find solutions to $\varphi\left(n\right)=2^{32}$

Published on 13 Jul 2018 - 7:56

198

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Are there further primes of the form $\varphi(n)^{\varphi(\varphi(n))}+1$?

Published on 26 Jul 2018 - 16:06

List Question

Extention of Totient Function to Reals

On the equation $\varphi(n)=\left(\frac{1+\sqrt{1+8n}}{8}\right)\cdot\left(\operatorname{rad}(n)-\frac{1+\sqrt{1+8n}}{2}\right)$

Prove or refute that $\sum_{n=1}^\infty\frac{1}{n^2+A\varphi(n)+B}$ will be irrational for some choice of integers $A,B\geq 1$

RSA decryption coefficient

An asymptotic about the recurrence $a_{n+1}=n\varphi(a_n)+a_{\varphi(n)}$, with $a_1=1$ and being $\varphi(m)$ the Euler's totient function

Euler Totient Integer Remainder Sum Lemma

Totient values of consecutive positive integers forming a pythagorean triple

A conjecture about Euler's function

Around the equation $4\,\varphi \left(2^{n-1} \sigma(n)\right) ^2=2^{\sigma(n)}\cdot\varphi(n)^2$

Calculate modulo solution of a number with a high exponent

Does a number have a primitive root if and only if φ(n)=λ(n)?

Do $4$ consecutive positive integers with square totient-value exist?

Conditions for computing $n$ given $\varphi\left(n\right)$

Find solutions to $\varphi\left(n\right)=2^{32}$

Are there further primes of the form $\varphi(n)^{\varphi(\varphi(n))}+1$?

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